When the poll asked what the Republican leadership in the Senate should do in response to a nomination, respondents were much more in favor of the Senate holding hearings than not -- 66 percent reported that the to 32 percent.

President Obama has said he will nominate someone to the Supreme Court soon, but Senate Majority Leader Mitch McConnell said the seat should remain unfilled "until we have a new president."

While Obama and Vice President Biden met with Senate leaders about the vacancy on Tuesday, the meeting ended without a breakthrough.

See potential replacements who could fill the Supreme Court vacancy

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Potential replacements for Justice Scalia, SCOTUS

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Poll: Americans want Obama to nominate a Supreme Court justice

Sri Srinivasan, Federal appeals court judge

(United States Department of Justice)

District Judge Ketanji Brown Jackson

(Photo via the United States District Court for the District of Columbia)

Loretta Lynch, the current U.S. Attorney General.

(Andrew Harrer/Bloomberg via Getty Images)

Paul Watford, currently a U.S. circuit judge for the Ninth Circuit.

(Photo by Bill Clark/Getty Images)

Jacquline Nguyen, the first Vietnamese American woman named to the state court in California.